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Neutrino properties

Glenn Horton-SmithKSU 4:30 Wednesday Math Seminar

Part I: April 13, 2011Part II: April 20, 2011

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Outline of Known Properties

● Three light neutrino “flavors”: νe, ν

μ, ν

τ

– All three are at least 5 powers of 10 less massive than the electron. (Cosmologists say at least 6.)

● Only see interactions of left-handed neutrinos (νL), right-

handed anti-neutrinos (νR)

● No evidence for νR or νL

.

– If they exist, then they are “sterile”, or very heavy, or both.● Mixing of the three neutrino flavors in vacuum

● At least two mixing modes: ν1-ν

2 seen in ν

e , ν2-ν

3 in ν

μ

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Outline of Unknown Properties

● Is there mixing of 1-3, and if so, how much? ***● Are there additional (sterile) light neutrinos? ***● What is the mass hierarchy of the neutrinos? **● Is there a Majorana mass term for neutrinos?*● Are there heavy (possibly RH) neutrinos?

(The number of *s indicates how much I know about the experiments that are supposed to address these issues.)

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Key Place for Review of Particle Properties

● http://pdg.lbl.gov -- Particle Data Group● Publishes the Review of Particle Physics.

– Citation for latest published version: K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010) .

● Chapter 13: Neutrino Mass, Mixing, and Oscillations● Completely rewritten by new authors in most recent edition!

● Also has tables of experimental results, and separate articles for “Neutrinoless Double-Beta Decay” and “The Number of Light Neutrino Types”.

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Outline of the neutrino chapter from the Review (for comparison)

. NEUTRINO MASS, MIXING, AND OSCILLATIONS

. 1. Introduction: Massive neutrinos and neutrino mixing

. 2. Neutrino oscillations in vacuum

. 3. Matter effects in neutrino oscillations (in Earth and Sun)

. 4. Measurements of solar Δm² and θ

. 5. Measurements of atmospheric |Δm²| and θ

. 6. Measurements of θ13

. 7. The three neutrino mixing, including the “see-saw mechanism”, the baryon asymmetry of the Universe, and the nature of massive neutrinos

. 8. Outlook

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What I will try to summarize

. NEUTRINO MASS, MIXING, AND OSCILLATIONS

. 1. Introduction: Massive neutrinos and neutrino mixing

. 2. Neutrino oscillations in vacuum

. 3. Matter effects in neutrino oscillations (in Earth and Sun)

. 4. Measurements of solar Δm² and θ

. 5. Measurements of atmospheric |Δm²| and θ

. 6. Measurements of θ13

. 7. The three neutrino mixing, including the “see-saw mechanism”, the baryon asymmetry of the Universe, and the nature of massive neutrinos

. 8. Outlook

Neutrinos as elementary particles

Neutrinos are very different from other elementary particles. Why? Knowing more about them should help.

stable constituents

of matter

Neutrinos

● Neutrinos have been seen from the sun, from nuclear power stations, from cosmic rays, from accelerators, and even from a supernova. Because they are almost “unstoppable”, we can use them to...

➢ ... peer inside the Sun.➢ ... detect supernovae and

other exciting things. ➢ ... radioassay a huge

sample of the Earth’s crust.

Neutrino interactions●The neutrino is the most difficult to detect particle that has ever been directly observed.

●Neutrinos are emitted in certain nuclear and particle decays.

●Neutrinos hardly interact with matter at all: a typical anti-neutrino from radioactive decay can pass through ~1014 km (~10 light years) of lead.

n pν

e

e-

Neutron beta decay

How can we detect neutrinos, even in principle?

● Although they hardly interact at all, they do interact.

● For any interaction or decay that makes a neutrino, there is a corresponding one that absorbs one.

● There are also neutrino scattering interactions.

n pν

e

e-

Neutron beta decay

pnν

e

e+

“Inverse” beta decay

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More interactions of the neutrino

n pν

e

e-

214Bi 214Poν

e

e-

65Zn 65Cuν

e

e+

8B 8Be*

νe

e-

μ- νμ

νe

e-

“Beta decay” of a muonBeta decays & electron capture

pnν

e

e+

“Inverse” beta decay

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Existence of “flavors”● Notice all of the interactions conserve the

total number of electron-type leptons and the number of muon-type leptons.

● “Lepton numbers” individually conserved:

● Le = Ne- + Nνe - Ne+ + Nνe

● Lμ = Nμ- + Nνμ - Nμ+ + Nνμ

● Also one for the “tau” lepton flavor.● If we didn't have separate muon and electron neutrinos, then the muon

could decay to an electron + photon.

● Limits on non-conservation in interactions ~10-12 level. (See “Tests of Conservation Laws” in Review.)

μ- νμ

νe

e-

“Beta decay” of a muon

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The masses of the known neutrinos

● Direct limits on electron (anti)neutrino masses come from tritium beta decay. PDG evaluation: <2 eV, 95% CL.

● Limits on muon and tau neutrino masses come from particle decays: <0.19 MeV and <18 MeV, resp.

● Limits on sum of all neutrino masses come from cosmology, range < 0.2~1 eV depending on model assumptions.

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Helicity of the neutrinos

● A fermion (1/2 spin) can have +1/2 or -1/2 spin along the direction of its motion: right-handed (RH) or left-handed (LH) helicity.

● Every observed interaction supports the model that interactions happen only with LH neutrinos or RH antineutrinos.

● Mathematically, this is implemented in the “standard model” by a factor (1-γ5) that zeroes out the amplitude of any interaction with a RH neutrino or LH antineutrino.

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A closer look at neutrino interactions

● The interactions of neutrinos with other particles is mediated by the Z and W bosons.

● The high mass of the Z and W result in low interaction cross-sections at low energy.

pnν

e

e+

“Inverse” beta decay

ud

νe e+

W+

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The number of light flavors

● The width of Z boson decays depends on the number of neutrinos the Z can decay into.

– Calculate the “invisible” decay mode partial width from the visible decays and the total width.

– To reduce model dependence, look at ratio of “invisible” to observed leptonic partial width.

● Result: # neutrinos = 2.984 ± 0.008.● Only counts neutrinos less massive than the Z.

Neutrino oscillations

νe

νμ

ντ

L/E (km/MeV)

P e e=1−sin2 212sin2 m122 L

4 E

In vacuum, a beam of pure electron neutrinos will seem to “disappear” and reappear according to:

Dense matter can change the effective values of θ and Δm2 for electron neutrinos. (But not other neutrinos.)

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Neutrino oscillations in vacuum(basic QM theory)

● This is attributed to the lepton flavor states being a mixture of the neutrino mass states.

[ | νe>| νμ>| ντ> ]= [U e1 U e2 U e3

U μ1 U μ 2 U μ 3

U τ1 U τ 2 U τ 3] [ |ν1>|ν2>|ν3> ]

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The two-neutrino system

● The neutrino state that interacts solely with electrons, νe, is a mixture of mass states.

● This leads to beats as the neutrino propagates.

[ |e >| >]=[ cos sin

−sin cos ][ |1 >|2 > ]

P e e L=∣⟨e L∣e 0⟩∣

2=1−sin22 sin2 m22−m1

2L4 E

Oscillation between source and detector

P ν̄e→not ν̄e=sin2 2θsin2 Δm2 L

4 E

distance L

Neutrino source: sun, reactor, accelerator, cosmic ray, ...

Neutrino detector observesrate and spectrum.

Analyze deficit or appearanceto look for oscillation.

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Evidence for two-neutrino oscillation(“solar” type)

● KamLANDKamLAND sees a clear oscillation signature in electron antineutrinos from many reactors at L~180 km, E=1.8~8 MeV.

● Also, SNO sees effect on solar νe.

Phys. Rev. Lett. 100, 221803 (2008)

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Evidence for another “two-neutrino” oscillation mode (“atmospheric” type)

● MINOS and Super-K see clear “disappearance” of muon neutrinos at L=735 km, E=1~50 GeV. Oscillation favored (3.7σ).

MINOS http://www-numi.fnal.gov/PublicInfo/forscientists.html, 2009/09/19.

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The “bi-mixing” matrix

● Two “rotations”: one about the 3 axis, and another about the resulting “1” (e) axis.

● θ23 = 45º±6º, θ12 = 34.5º±1.3º.

● Compare to quarks: θus = 12.9º±0.2º, θcb = 2.4º±0.1º.

[ | νe >| νμ >|ντ>] = R1(θ23)R3(θ12)[ |ν1 >

| ν2 >| ν3 >]

= [ cosθ12 sinθ12 0−cosθ23 sinθ12 cosθ23 cosθ12 sinθ23

sinθ23 sinθ12 −sinθ23 cosθ12 cosθ23][ |ν1 >

| ν2 >| ν3 >]

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Break

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Neutrino properties II

Glenn Horton-SmithKSU 4:30 Wednesday Math Seminar

April 20, 2011

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Mixing matrix with two mixing angles

● Two “rotations”: one about the 3 axis, and another about the resulting “1” (e) axis.

● θ23 = 45º±6º, θ12 = 34.5º±1.3º.

● Compare to quarks: θus = 12.9º±0.2º, θcb = 2.4º±0.1º.

[ |νe >|νμ>|ντ>] = R1(θ23)R3(θ12)[ |ν1 >

| ν2 >|ν3 >]

= [ cosθ12 sinθ12 0−cosθ23 sinθ12 cos θ23 cosθ12 sinθ23

sinθ23 sinθ12 −sin θ23 cosθ12 cosθ23][ |ν1 >

| ν2 >|ν3 >]

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This is pretty close to the so-called “tribimaximal” matrix

[ | νe >| νμ>| ντ>] = [ √

23 √ 1

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−√ 16 √ 1

3 √ 12

√ 16−√ 1

3 √ 12][ |ν1 >

| ν2 >| ν3 >]

● “Trimaximal” in equality of m

2

components of all three flavors.

● “Bimaximal” in full mixing of 2 and 3 in mu/tau oscillations.

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The general mixing matrix, without complex phases

● sin θ13 represents amount of ν

3 in ν

e.

[ |νe >|νμ>|ντ>] = R1(θ23)R2(θ13)R3(θ12)[ | ν1 >

|ν2 >| ν3 >]

= [ c12 c13 s12 c13 sin θ13

−c23 s12−c12 s13 s23 c12 c23−s12 s13 s23 c13 s23

s12 s23−c12 c23 s13 −c12 s23−c23 s12 s13 c13 c23][ | ν1 >

|ν2 >| ν3 >]

Here cij≡cosθij , sij≡sin θij

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Three-component mechanical analogies

● Three coupled pendulums● Coupling through springs● Only two of three modes

move central mass. (θ13=0)

● 3d mass-on-springs● “Coupling” through rotation● Arbitrary rotation would

couple all three. (θ

13= anything)

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Existing 90% limits on sin θ13

● Experiments measure sin2 2θ13.

● Best direct limit is from CHOOZ (1999): a 5 ton detector at 1 km from two 4.3 GWth reactors.

Experiment sin2 2θ13

sin θ13

CHOOZ <0.19 <0.22Palo Verde <0.36 <0.32MINOS <0.42 <0.35Global fit to all neutrino data

0.06±0.04or <0.12

0.12±0.04or <0.18

Experiment

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Some new experiments to study θ13

● Double ChoozDouble Chooz, Daya Bay, and RENO are multi-detector, multi-reactor experiments.

● T2K and NOνA are experiments using muon neutrinos made by accelerators, like MINOS.

Experiment Mass and power sin2 2θ13

90% limit

Double ChoozDouble Chooz 10t, 8.6 GWth 0.10 (Phase 1)0.03 (Phase 2)

Daya Bay 80t, 18 GWth 0.01RENO 30t, 16 GWth 0.02T2K, NOνA muon neutrinos 0.004~0.02

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Projected sensitivity vs time of new experiments to study θ

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● Plot by Huber, et al, arXiv:0907.1896v1, July, 2009, based on information from each collaboration. Move Double ChoozDouble Chooz line ~0.5 year to the right, Daya Bay a little more; move others...?

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Beyond θ13

: complex phases

● Neutrino wavefunctions incorporate complex numbers. A three-neutrino mixing matrix can have up to three complex phases.

● They're commonly called δCP, α

1, and α

2.

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The most general three-neutrino mixing matrix

● δCP breaks “charge-parity” symmetry.

● The α1 and α

2 are only important if neutrinos can

become antineutrinos. (“Majorana mass term”.)

[ |e >|>

|> ] = U [ |1 >|2 >|3 > ]

U = [ c12 c13 c13 s12 sin13 e− i

−c23 s12−c12 s23 s13 ei c12 c23−s12 s23 s13 e i c13 s23

s12 s23−c12 c23 s13 ei −c12 s23−c23 s12 s13 e i c13 c23]

× diagei1 , ei2 ,1 .

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What is “CP”?

● Every particle has a corresponding antiparticle: e+ for e-, ̅ν for ν, etc. If swapping particles for antiparticles doesn't change an interaction, that's C symmetry.

● Particles have spin. If inverting the spin of all particles doesn't change an interaction, that's P symmetry.● Remember, active neutrinos are all left-handed,

antineutrinos are all right-handed.

● CP is doing both C and P.

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OK, if that's CP, what happens if it's broken?

● δCP affects antineutrinos differently

from how it affects neutrinos.● Plot at right shows the theoretical

probability (in %) in T2K of neutrino oscillation compared to antineutrino oscillation, for various values of δ

CP ,

assuming sin2 2θ13=0.05.

● Diagonal green line = no CP breaking.

H. Minakata and H. Nunokawa, JHEP 0110, 001 (2001).

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What does that have to do with matter What does that have to do with matter in the universe?in the universe?

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● As the universe expands, it cools.

● At high temperatures, T>>mc2, particle-creating interactions can be in equilibrium with absorption and annihilation.

● This equilibrium disappears as the universe cools. (Neutrinos actually go in and out of equilibrium because it takes them a long time to equilibrate.)

● Similarly, atoms only form once the universe has cooled enough. We see the cosmic microwave background (CMB) from 380,000 years after the Big Bang; before that, the universe was opaque.

● The CMB is so uniform that there must have been a rapid “inflation” earlier.

A very quick, simplified review of Big Bang cosmology

time Image credit: WMAP/NASA.

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The matter mystery

● The universe is exclusively matter, except for antimatter-matter pairs made in collisions of matter and photons.

● If all interactions during inflation conserved C, CP, and “baryon number”†, this would not be the case! In fact, any initial matter-antimatter asymmetry would be almost entirely erased.

● We need some particle, out of equilibrium during inflation, with a large violation of CP.

† Baryon-number violation is “expected to be contained in grand unified theories as well as in the non-perturbative sector of the Standard Model.” [Review of Particle Physics]

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Experiments to measure δCP

● T2K, “Tokai to Kamioka” (Japan):295 km, 0.75 MW beam power.

● NOνA, Fermilab to Minnesota (US): 810 km, 0.7 MW beam power.

● Good news: Great sensitivity to CP, ordering of neutrino masses, and θ

13.

● Bad news 1: sensitive to all three at the same time.

● Bad news 2: if θ13=0, no sensitivity to CP.

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Projected “discovery potential” vs time of new experiments

● Again from Huber, et al, arXiv:0907.1896v1, July, 2009.

● Depending on δCP, T2K and NOvA might see a θ

13≠0 effect, yet not

know what θ13 is, unless Double ChoozDouble Chooz or Daya Bay tells them!

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Projected “discovery potential” vs time of new experiments

● Again from Huber, et al, arXiv:0907.1896v1, July, 2009. 90% CL. (!) Normal hierarchy plots shown, see original for inverted hierarchy.

● We are very interested to know if sin2 2θ13<0.03.

Mass hierarchy “discovery” CP violation “discovery”

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OK, so let me get this straight...

● If θ13 is non-zero, then δ

CP has meaning.

● And if so, then neutrinos violate CP.● And if that effect is big enough, then that would

prove that neutrino CP violation is the cause of the matter-antimatter asymmetry of the Universe, right?

Er... not quite that last bit.

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The matter-antimatter asymmetry model depends on CP violation in heavy

neutrinos● Our familiar, almost-massless neutrinos turn out not to be

able to do the job in any model that's been put forth.

● There are “attractive theoretical considerations”† that lead one to hypothesize heavy partners to the light neutrinos. (“See-saw model”, etc.)

● CP violation in these heavy neutrinos could do the job.‡

† I.e., there is more reason to hypothesize heavy neutrinos than just lack of proof that they don't exist. ‡ No proof that it's not so, yet.

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The see-saw mechanism

1. Add an explicit mass term only for right-handed-neutrinos—left-handed-antineutrinos, and make it really big so we don't see them at “low” energies.

2. Couple RH and LH neutrinos to Higgs.

3. Interplay gives LH neutrino mass matrix m

ij ~ mD

i mD

j / MRH, where mD is essentially the mass

the neutrino would get from the Higgs mechanism without the explicit RH neutrino mass.

4. In case of multiple RH neutrinos, you have multiple MRH, and also a matrix of Higgs couplings λ

ij.

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The matter-antimatter asymmetry

● Taking mD ~ “normal” masses and m~0.1 eV, we have MRH ~ 1014 GeV. (The GUT theorists think this is good.)

● Because the heavy neutrinos Nj are (hypothetically) so

massive, they can decay into other particles.

● The couplings λij are allowed to have CP-violating

phases, so these processes can have different rates.● Another process in the standard model then turns this into baryon

asymmetry.

N j→ l++Φ-

N j→ l -+Φ+

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This model is actually not so bad

● CP violation in heavy neutrinos leads to an imbalance of matter vs. antimatter in the very early universe, with only a little bit of “new physics”.

● This is called leptogenesis.● I'm not aware of a viable model with a better

“testable hypotheses to total hypotheses ratio.”– The biggest fly in the ointment is that CP violation in light

neutrinos doesn't tell us everything about λij, so we can't prove or disprove CP violation for the heavy neutrinos that way.

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A modest research program to address the “leptogenesis” question

A) Measure θ13. [* We are here.][* We are here.]

Forget step B if θ13 is too small.

B) Measure δCP of ordinary neutrinos.

C) Search for evidence of other neutrinos. [*][*]

D) Search for evidence that some are heavy.

E) Search for evidence of CP violation in heavy neutrinos, and/or unique signatures of this effect on early universe. [how to do this is unclear at present]

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Near- and Mid-Term Outlook

● New reactor experiments to search for disappearance of electron antineutrinos: Double Chooz (now taking data), RENO, Daya Bay.

● Longer term accelerator experiments to search for electron neutrino appearance and make more precise measurements of other parameters and mass hierarchy.

● Neutrino-less double beta decay experiments also searching for evidence of Majorana nature of neutrinos (ν-ν equivalence).

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A far-range outlook from the neutrino chapter in the Review

● Determine Majorana or Dirac nature● Determine mass hierarchy● Determine absolute scale of mass

● Measure θ13 or improve limit by factor of 10.

● Determine CP symmetry broken/unbroken for ν.● Measure all mixing parameters more precisely.● “Understanding at a fundamental level the

mechanism giving rise to neutrino masses and mixing and to L−non-conservation.”

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